Above is meant to be the whole fraction to the power 2, but i was having some Latex Syntax problems showing that (Thinking)

I have tried changing $\displaystyle s^j$ and $\displaystyle p^j$ to $\displaystyle ps^j$and taking it outside the summation when beginning to try and find the PGF but i didnt get anywhere, help needed please! (Nod)

Also maybe $\displaystyle \Sigma$ $\displaystyle (j+1)$$\displaystyle a^j$$\displaystyle {(1-a)}^2$ = 1 for any a where $\displaystyle \mid$a$\displaystyle \mid$ < 1 can be used? i cant see how though!

Above is meant to be the whole fraction to the power 2, but i was having some Latex Syntax problems showing that (Thinking)

I have tried changing $\displaystyle s^j$ and $\displaystyle p^j$ to $\displaystyle ps^j$and taking it outside the summation when beginning to try and find the PGF but i didnt get anywhere, help needed please! (Nod)

Also maybe $\displaystyle \Sigma$ $\displaystyle (j+1)$$\displaystyle a^j$$\displaystyle {(1-a)}^2$ = 1 for any a where $\displaystyle \mid$a$\displaystyle \mid$ < 1 can be used? i cant see how though!

The trick in these is to differentiate the geometric, that brings downs that power of j.